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McGraw Hill Glencoe Algebra 1, 2012

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McGraw Hill Glencoe Algebra 1, 2012 View details

Standardized Test Practice

Exercise 10 Page 71

Pay close attention to the order of operations.

$20$

Practice makes perfect

According to the order of operations, powers are evaluated before multiplication and division, while addition and subtraction are evaluated last.

\frac{5 ^{3} \cdot 4 ^{2} - 5 ^{2} \cdot 4 ^{3}}{5 \cdot 4}

In this case we have a fraction, which can be considered a grouping symbol. Therefore, we will evaluate the expressions in the numerator and denominator individually before completing the division. Notice also that even within these expressions, we must obey the order of operations.

5^{3} \cdot 4^{2} - 5^{2} \cdot 4^{3}

For this, we must remember to evaluate the exponents first, the multiplication next, and finally the difference between their results.

Operation	Before Simplification	After Simplification
Calculate power	$\frac{5 ^{3} \cdot 4 ^{2} - 5 ^{2} \cdot 4 ^{3}}{5 \cdot 4}$	$\frac{1 2 5 \cdot 1 6 - 2 5 \cdot 6 4}{5 \cdot 4}$
Multiply	$\frac{1 2 5 \cdot 1 6 - 2 5 \cdot 6 4}{5 \cdot 4}$	$\frac{2 0 0 0 - 1 6 0 0}{2 0}$
Subtract term	$\frac{2 0 0 0 - 1 6 0 0}{2 0}$	$\frac{4 0 0}{2 0}$
Calculate quotient	$\frac{4 0 0}{2 0}$	$20$

The expression equals

20 .

Alternative Solution

Using a Calculator

We can also evaluate this expression using a calculator. To do so, type it as shown below.

Subchapter links

Multiple Choice p.70

Short Response/Gridded Response p.71

Extended Response p.71